Einstein Physics

8/10/2019 Einstein Physics

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Ta-Pei Chengtalk based on

Oxford Univ Press (2013)

Einsteins PhysicsAtoms, Quanta, and Relativity --- Derived,

Explained, and Appraised


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1. Atomic Nature of Matter

2. Quantum Theory

3. Special Relativity4. General Relativity

5. Walking in Einsteins Steps

The bookexplains his physics

in equations

Albert Einstein

1879 1955

Todays talkprovides w/o math details

some highlight

historical context& influence

1. The quantum postulate: Planck vs Einstein

2. Einstein & quantum mechanics

3. Relativity: Lorentz vs Einstein

4. The geometric theory of gravitation5. Modern gauge theory and unification


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Blackbody Radiation cavity radiation = rad in thermalequilibrium

Einstein, like Planck, arrived at the quantum hypothesis thru the study ofBBR

Kirchhoff (1860) densities

= universal functions rep intrinsic property of radiation

2nd law ),(and)( TTu

=0

),()( dTTu

Stefan (1878) Boltzmann (1884) law:Thermodynamics + Maxwell EM (radiation pressure = u/3)

electromagnetic radiation = a collection of oscillators u = E2, B2 ~ oscillator energy kx2

oscillating energy ~ frequency : Their ratio of is an adiabatic invariant

4)( aTTu =

Wiens displacement law (1893))/(),( 3 TfT =

3

Wiens distribution (1896): fitted data well. until IRTeT /3),( =

1),(

/

3

=

Te

T

What is the f function?

To find the u(T) and (T,) functions:

=0

),()( dTTu


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Blackbody Radiation Planck (1900):1

),(/

3

=T

e

T

4

,...2,1,0 == nnh

entropy/)8/( 23 STdUdScU and ==

10

Einsteins 1905 proposal of light quanta

wasnot a direct follow-up of Plancks


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Einsteins 1905 proposal of light quanta h=

Rayleigh-Jeans = the low frequency limit of the successful Plancks distribution

Einstein used Plancks calculation and

invoked the equipartition theorem ofstat mech

to derive the Rayleigh-Jeans law:

noted its solid theoretical foundationbut

poor accounting of the data, notably the problem of ultraviolet catastrophe

238 kTc=

==0

du

( )23 8/cU=kTU

2

1=

showing BBR = clear challenge to classical physics

5

The high frequency limit (Wiens distribution )

Einstein undertook a statistical study of (BBR)wien :

instead of W, calculate due to volume change (BBR)wien ~ ideal gas

(BBR)wien=a gas of light quanta with energy of

Einstein arrived at energy quantization independently---- cited Planck only in 2 places

A year laterEinstein gave a new derivation of Plancks distribution

nh=

new physics

S

Te /3 =


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Einsteins discoveries in quantum theoryEinsteins photon idea was strongly resisted

by the physics community for many years

because it conflicted with the known

evidence for the wave nature of lightMillikan, Planck,

(1900) Planck: is onlya formal relation

(1905)

Einstein: the quantum idea mustrepresent new physicsproposed photoelectric effect as test

beyond BBR: Q theory of specific heat (1907)

h=

Einstein stated for the 1st time:

quanta carried by point-like particles

point of view of Newtonian emission theoryPhoton carries energy + momentum /hp=

(1913) Bohrs quantum jumps describe

absorption and emission of photons

(191617) Einstein construct a microscopictheory of radiationmatter interaction:

(A and B coeff); The central novelty and

lasting feature is the introduction of

probability in quantum dynamics

(192425) Bose-Einstein statistics

& condensation

6

General acceptance of the photon idea

Only after Compton scattering (1924)

15

h as conversion factor particle wave


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Modern quantum mechanics :

states = vectors in Hilbert space (superposition)

observables = operators (commutation relations)

Classical radiation field

= collection of oscillators

Quantum radiation field

= collection of quantum oscillators

hnEn )( 21

+=

His discoveries in quantum theory:Wave/particle nature of light,

quantum jumps etc. can all beelegantly accounted for in the framework of

quantum field theory

QFT description broadens the picture of interactions

not only can alter motion, but also allows for

emission and absorption of radiation

creation and annihilation of particles Alas, Einstein never acceptedthis neat resolution

as he never accepted

the new framework of QM

A firm mathematical foundation for Einsteins photon idea Quantum jumps naturally accounted for by ladder operators

[ ] 1~,, behaviorparticlennahaa = +

Einstein & Quantum Mechanics

7

Beautiful resolution of wave-particle duality

in radiation energy fluctuationikx

eawave ~

8


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Einstein & QM: The debatewith

Bohr

Bells theorem (1964) : these seemingly philosophical questions could lead to

observable results. The experimental vindication of the orthodox interpretation has

sharpened our appreciation of the nonlocal features of quantum mechanics.

Einsteins criticism allowed a deeper understanding of the meaning of QM.

Nevertheless, the counter-intuitive picture of objective reality as offered by QM

still troubles many, leaving one to wonder

whether quantum mechanics is ultimately a complete theory.

Einstein, Podolsky & Rosen (1935) : A thought experiment highlighting the

spooky action-at-a-distance feature: the measurement of one part of an entangled

quantum state would instantaneously produce the value of another part, no matter how

far the two parts have been separated. the discussion and debate of EPR paradox have

illuminated some of the fundamental issues related to the meaning of QM

Orthodox interpretation of QM (Niels Bohr & co): the attributes of a physical object

(position, momentum, spin, etc.) can be assigned only when they have been measured.

Local realist viewpoint of reality (Einstein,): a physical object has definite attributes

whether they have been measured or not. . QM is an incomplete theory

20

8

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9/21

Special

RelativityMaxwells equations: EM wave c Contradict relativity?

2 inertial frames x = x - vt & d/dt = d/dt velocity addition rule u = u -

v

The then-accepted interpretation: Max eqns valid only in the rest-frame of ether

12SR 1

Key Q: How should EM be described for sources and observers

moving with respect to the ether-frame?

The electrodynamics of a moving body

9

vtxx =' xc

vtt

2' =

A very different approach by Einstein

Michelson-Morley null result @ O(v2/c2) length contraction

[ + a math construct local time]

Lorentz transformation Maxwell covariant to all orders (1904)

( )vtxx ='

= x

c

vtt

2'

1

2

2

1

=

c

v

Still in the framework of ether Applicable only for EM

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Special Relativity

Dispense with etherInvoke theprinciple of relativity

Einsteins very different approach

Relativity is a symmetry in physicsPhysics unchanged under some transformation

Relativity = same physics in all coordinate frames

How to reconcile (Galilean) relativity u = u - vwith the constancy ofc?

Resolution: simultaneity is relative

Time is not absolute, but frame dependent t t

From this 1905 realization to full theory in 5 weeks 10yrsRelation among inertial frames

correctly given by Lorentz transformation,with Galilean transformation as low v/c approximation

All nontrivial results follow from this new conception of time

The new kinematics applicable to all physics

With a keen sense of aesthetics in physics

Einstein wastroubled by

Dichotomy of matter ~ particles, radiation ~ waves

Light quanta

EM singles out 1 particular frame: the ether frame

Case I: moving charge inB (ether frame)

Lorentz force (per unit charge)

Case II: changingB induces anE via

Faradays law, resulting exactly the

same force, yet such diff descriptions

Bve

f

=

Magnet-conductor thought experiment

Seeking a more symmetric picture

valid in all frames

25

10

11


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Even simpler perspective

Hermann Minkowski (1907)

Essence of SR: time is on an equal footing asspace.

To bring out this symmetry, unite them in a single math structure, spacetime

Geometric formulation

Special

Relativity

Einstein was initially not impressed,calling itsuperfluous learnedness

SR: The arena of physics is the

4D spacetime

.. until he tried to formulate

General relativity (non-inertial frames)

= Field theory of gravitation

Gravity = structure of spacetimeSR = flat spacetime

GR = curved spacetime

11

Emphasizes the invariance of the theory: c s

Lorentz-transformation = rotation in spacetime

metric [g] all SR features

[ ][ ][ ]

( ) 2

222222

1

1

1

1

length

z

y

x

ct

zyxct

xgxzyxtcs

=

=

=+++=

R

c as the conversion factor space time

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12/21

The Equivalence Principle (1907)

played a key role in the formulation ofgeneral theory of relativity

Why does GR principle automatically

bring gravity into consideration?

How is gravity related to spacetime?

starting from Galileo Remarkable empirical observation

All objects fall with the same acceleration

Gravity disappears in a free fall frame

EP: Motion in grav field totally independent ofproperties of the test body,

attributable directly to underlying spacetime?

Einstein proposed in 1912:gravitational field = warped spacetime

a = g

accelerated frame = inertial frame w/ gravity

EP as the handle of going from SR to GR

Einstein: My happiest thought

SR GR, flat curved spacetime

12

30

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13/21

Relativity

as a coordinate symmetry

Special relativityflat spacetime

= spacetime-independent transformation

Global symmetryR

Must replace ordinary derivative by

covariant differentiation

[ ] [ ][ ] g

basesmovingthecompensate=

+= dDd

inbroughtisgravity

with DdGRSR

local symmetry dynamics

Equations written in terms of 4-tensorsare automatically relativistic

General relativity

curved spacetime with moving basis vectorsgeneral coord transf = spacetime dependent

Local symmetry)( xRR =

13

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14/21

Source particle Curved spacetime Test particleEinstein

field eqn

Geodesic

Eqn

gravitational field = warped spacetimemetric tensor [g

] =

rela. grav. potential

T energy momentum tensorNg Newtons constant

1915

G curvature tensor = nonlinear 2nd derivatives of [g]Metric being gravi pot,

Curvature = tidal forces

The Einstein equation

10 coupled PDEssolution = [g

] TgG N=

Field eqnEqn of

motion

Source particle Field Test particle

Field theory of gravity

35

14

General Relativity

gNas the conversion factor geometrymass/energy

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15/21

In the limit of test particles moving with v cin a static and weak grav field

Einstein Newton (the 1/r 2 law explained!)

GR can depict new realms of gravity:

time-dep & strong

time-dep: GR gravitational waveHulse-Taylor binary pulse system

Strong: Black Holes full power & glory of GR

Role of space and time is reversedLight-cones tip over instead of (t = ), (r = 0)

Even light cannot escape

The Einstein field equation

TgG N=General Relativity

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16/21

Einstein & unified field theorythe last 30 years of his life , strong conviction:GR + ED solving the quantum mystery?

The symmetry principleBefore Einstein, symmetries were generally regarded as

mathematical curiosities of great value to crystallographers, but

hardly worthy to be included among the fundamental laws ofphysics. We now understand that a symmetry principle is

not only an organizational device,

but also a method to discover new dynamics.

Was not directly fruitful, but his insight Symmetry & Geometry

fundamentally influenced effort by others:Gauge theories and KK unification, etc.

But both possible only with modern QM

40

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Gauge TheoryRelativity

Transformation

in coordinate space

Gauge symmetry

Local transformation

in the internal charge space

changing particle label

R )( xR

Gauge principle:

Change from global to local

transformation on QM states

brings in the compensating field A ,

thegauge field

[ ] [ ]AdDd +=[ ] [ ][ ]

g

basesmovingcompensate

localglobal

=

+=

dDd

GRSR

SR + gauge principles Maxwell

Electrodynamics as a gauge interaction

Gauge principle can be used to extend consideration to other interactions

)(singlea)(

xAeRxi =

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18/21

Particle physics

Special relativity, photons, & Bose-Einstein statistics = key elementsBut Einstein did not work directly on any particle physics theory

Yet, the influence of his ideas had been of paramount importance

to the successful creation of the Standard Model of particle physics

45

Strong, weak & electromagnetic interactions

are allgauge interactions

Symmetry principle allowed us to discover the basic eqns of SM

QCD, electroweak field eqns = generalization of Maxwells eqns

Non-commutative transformation:

Multiple gauge (Yang-Mill) fields

Spontaneous symmetry breaking:

The symmetry is hidden

Quantization & renormalization

truly relevant degrees of freedom

for strongly interacting particles are

hidden (quark confinement)

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19/21

Kaluza-Klein theory

unification of GR+Maxwell1919 Theodor Kaluza : GR in 5D

extra dimension w/ a particular geometry[g]kk

GR5kk

= GR4 + ED4The Kaluza-Klein miracle!

In physics , a miracle requires an explanation

1926 Oskar Klein explained in modern

QM

*Gauge transf = coord transf in extra

D *Internal charge space = extra D

Foreshadowed modern unification

theories

GR + SM requirecompactified multi-dim extra D space

Einsteins

influence lives on!

Compactified extra D a tower of KK

states

the decoupling of heavy particles

simplifies the metric to [g]kk

Q: What is the charge space?

Whats the origin of gauge symmetry?

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20/21

A pithy description

via the fundamental constants

h -- c --gN

sc

gt

cmc

gl

GeV

g

ccM

NP

NP

N

P

44

5

33

3

195

2

104.5

106.1

102.1

==

==

==

h

h

h

Natural units, not human construct

Dimensions of the fundamental theory

i.e. quantum gravity (GR + QM)

Last slide : summarizing

the central nature of

Einsteins physics

They are conversion factors

connecting disparate phenomena

All due to Einsteinsessential contribution

h: Wave & Particlec: Space & Time

gN: Energy & Geometry

(QT)

(SR)

(GR)

Besides his legacy on geometry

& symmetry principle,his fundamental contribution =

Ability to connect

disparate phenomena

form an unit system of

mass/length/time(The Planck unit system)

h = Plancks constant

gN =Newtons constant

c = Einsteins constant ?!

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These PowerPoint slides are posted @

www.umsl.edu/~chengt/einstein.html

US publication date = April 5, 2013

Hardback ISBN 0199669910

Copies of the book are left in

PSU Physics Dept Office

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